what-is-the-value-of-and-how-can-combute-erf-pi-

Question Number 127214 by mohammad17 last updated on 27/Dec/20

w h a t i s t h e v a l u e o f a n d h o w c a n c o m b u t e ?

e r f (π) ?

Answered by Olaf last updated on 27/Dec/20

\erf (x) = \frac{2}{\sqrt{π}} \int_{0}^{x} e^{- t^{2}} d t

(used in probabilities and statistics)

\erf (π) = \frac{2}{\sqrt{π}} \int_{0}^{π} e^{- t^{2} d t}

We can compute :

\erf (x) = \frac{2}{\sqrt{π}} \underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n}}{(2 n + 1) n!} x^{2 n + 1}

\erf (π) = \frac{2}{\sqrt{π}} \underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n}}{(2 n + 1) n!} π^{2 n + 1}

\erf (π) \approx 2 \sqrt{π} - \frac{2 π^{5 / 2}}{3} + \frac{π^{9 / 2}}{5} - \frac{π^{13 / 2}}{21} + o (π^{17 / 2})

Commented by mohammad17 last updated on 27/Dec/20

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